The present invention relates generally to fluid dynamics, and more specifically, to estimating the average velocity of a flowing fluid mixture from observed concentrations of a reacting constituent of the fluid.
A variety of devices and methods are available for measuring the volumetric flow rate of a fluid are available. Typical flow measurement devices include turbine meters, venturi meters, orifice plate meters, pressure drop measurements, ultrasonic meters, and flumes, among others. Flow measurement devices often are inserted into a pipe or flow channel. Such invasive techniques are inconvenient and expensive.
Some existing flow meters determine the flow rate of a fluid based on a comparison of the static pressure and the dynamic pressure of the fluid at a given location. Other flow meters are available that estimate the flow rate of a fluid based on a relationship between the fluid temperature and the kinematic viscosity of the fluid.
Still other fluid flow meters are available that determine the travel time of exhaust gas between two points by measuring the fluctuating concentration of a component gas in the exhaust flow at each of the two points. The exhaust gas velocity may be calculated based on the distance between the two points and the time required for the exhaust gas to travel between the two points.
Fluid flow control systems are available that use a reactive transport model to determine a desired flow rate in a fluid flow control system. A typical flow control system of this type uses a reaction-diffusion equation and a conservation of mass equation to model the chlorine concentration profile along a contact basin in order to determine the appropriate flow rate the system that will result in a desired concentration of chlorine in a location of the basin at a particular point in time.
In addition, fluid constituent concentration measuring instruments are available that use fluid temperature and flow rate as inputs to determine an applicable impedance change per unit time—particulate concentration constant from a predetermined table, which may be obtained in advance by experiment or calculated.
Some existing water distribution systems include relatively few sensors. This sparsity is especially prevalent for flow meters, because these often are expensive to install and costly to maintain. Flow meters often are available only at the inlet to a relatively expansive metered area of a distribution system. Even in cases where individual consumers have flow meters, sampling rates generally have low temporal resolution. The general lack of available flow measurement makes it difficult to evaluate usage and locate leakage. Nevertheless, in many water distribution systems, measurements of water quality parameters, such as chlorine concentration, have become more common.